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Abstract

Colloidal suspensions of nano-sized particles in a base fluid, nanofluids, have recently
gained popularity as cooling fluids mainly due to their enhanced heat transfer capabilities.
However, there is controversy in the literature on the reported properties of nanofluids
and their applicability, especially since there is no fundamental understanding that
explains these enhancements. A better understanding of these fluids and how they interact
with a solid boundary may be achieved by a detailed near-wall fluid flow study at
nanoscale. This work presents for the first time the near-wall velocity measurements
for nanofluids using nanoparticle image velocimetry. This novel technique uses evanescent
illumination in the solid–fluid interface to measure near-wall velocity field with
an out-of-plane resolution on the order of O(100 nm). Nanofluids of different concentrations
were prepared by dispersing silicon dioxide particles (10 to 20 nm) in water as the
base fluid. Initially, viscosity measurements were conducted for the prepared nanofluids.
The near-wall velocity data were then measured and compared with that of the base
fluid at the same flow condition. It was observed that even though nanofluid viscosity
had increased with particle loading, the near-wall velocity values were similar to
that of the base fluid for a given flow rate. Together, these measurements vindicate
the homogenous and Newtonian characteristics of the nanofluids in the near-wall region.
Despite the low particle concentrations investigated, the present work also discusses
the complexity involved in utilizing the methodology and possible errors arising during
experimentation so as to implement this measurement tool more effectively in the future.

Keywords:

nanofluids; nPIV; Newtonian fluid; viscosity; TIRF

Background

Thermal cooling is one of today’s most challenging technological problems, and there
has been a constant effort by the scientific community to improve the heat transfer
capabilities of cooling fluids. The notion that thermal conductivity of suspensions
increases with the total surface area of the particles in the suspension triggered
the concept of using nanosized particles in suspensions. This introduced a new class
of engineered fluids called nanofluids: colloidal suspensions of nano-sized particles
(approximately 5 to 100 nm) in a base fluid
[1]. The prevalent popularity of nanofluids in the heat transfer community has been due
to its reported anomalous thermal conductivity enhancement. Following the initial
development of nanofluids, several experimental reports have shown the great potential
of these fluids to be used for heat transfer applications
[2-9]. However, there have been several recent reports questioning the heat transfer enhancement
of nanofluids
[10-16]. These reports assert that nanofluids behave as a homogeneous mixture and that their
thermal properties can be successfully predicted by classical effective medium theories
[13].

Several theoretical models and explanations have been proposed to explain the anomalous
heat transfer characteristics of nanofluids. Brownian motion of nanoparticles in combination
with aggregation and diffusion theories have been claimed to be the major justifications
for the observed anomaly in thermal conductivity
[17]. Flattening of velocity profile, shear thinning, and thermophoretic forces in the
near-wall region have been asserted to be the probable causes for enhanced convective
heat transfer characteristics of nanofluids
[9,18,19]. However, it may be noted that most of the theoretically proposed models have not
been directly validated by experimental results. Gaining an understanding of the near-wall
flow field can help in better comprehending the phenomenon and assists in improving
the theoretical models used in predicting the enhanced heat transfer characteristic
of nanofluids. Walsh et al.
[20] used microparticle image velocimetry (μPIV)
[21] to obtain the velocity profile of nanofluids flowing inside a microchannel, d = 1,085 μm. However, the spatial, out-of-plane resolution of their work was from
4 to 30 μm and could not capture the flow velocities in the region very close to the
wall. To the best of the authors’ knowledge, there have been no other experimental
studies that have investigated the near-wall flow fields in nanofluids.

The evanescent wave-based PIV technique, also known as nanoparticle image velocimetry
(nPIV), is an extension of nPIV which can substantially improve the out-of-plane resolution
of the measurements close to the wall
[22]. Evanescent wave-based techniques, namely total internal reflection microscopy and
total internal reflection fluorescence (TIRF), have been widely used in biological
and surface science fields in the past for near-wall visualization
[23]. In nPIV, evanescent wave illumination generated by the total internal reflection
(TIR) of a laser beam at the fluid–solid interface is used to illuminate particle
tracers in the flow field with a spatial resolution on the order of O(100 nm). This
technique has been successfully implemented in the past in fluid velocimetry for studying
electro-osmotic flows through microchannels
[24,25], near-wall Brownian diffusion
[26], and the effect of the near-wall forces
[27].

Present work demonstrates applicability of nPIV to investigate flow behaviors very
near to the wall while using nanofluids. Near-wall measurements are reported for the
first time for silicon dioxide (SiO2)-water nanofluid flow inside a microchannel at varying particle concentrations and
flow rates with an out-of-plane spatial resolution of less than 300 nm. The results
are then compared with those obtained for the base fluid. These results, along with
the rheological characterization of the bulk nanofluids, are used to investigate occurrence
of any non-homogeneity in the flow characteristics of the nanofluids in the near-wall
region.

Theory

Similar to PIV, both μPIV and nPIV ‘track’ naturally buoyant fluorescent tracers to
measure fluid velocity with the assumption that they follow fluid flow faithfully.
As mentioned earlier, in nPIV, the evanescent wave generated at the glass water interface
is used to illuminate particles only in the near-wall region. A brief introduction
into the working principle behind nPIV follows.

When a light beam travels through a medium with a refractive index n1 into another transparent medium with a lower refractive index of n2 at an angle exceeding the critical angle θc = sin−1(n2/n1), it is totally reflected at the interface. However, the electromagnetic field penetrates
into the lower refractive index region and propagates for a small distance parallel
to the interface creating what is called an evanescent wave. This evanescent wave
is capable of exciting fluorescent particles in this region, while the large numbers
of particles farther away in the bulk liquid remain unexcited. One distinct characteristic
of the evanescence wave is its nonuniform intensity in the direction normal to the
interface, where the intensity, I, decays exponentially with distance, z, normal to the wall as follows:

(1)

I0 is the maximum intensity at the wall, and zp is the penetration depth:

(2)

where λ0 is the wavelength of the light, and θ is the incident angle. For visible light at a glass water interface, zp is on the order of O(100 nm) and is independent of the incident light polarization
direction. It can be seen that in addition to the incident angle of the light, penetration
depth depends on the refractive indices at the interface and the wavelength of light.
Figure
1 shows the schematic of a TIRF setup used in a nPIV experiment where only the near-wall
fluorescent particles in the fluid are excited and viewed from the bottom of the microscope
plate. The emission intensity of the tracer particles in this region is also an exponential
function of the distance from the wall with a decaying trend as stated by Equation
1. However, depending on the optical characteristics of the imaging system, ultimate
depth of visible region, zv, depends on the intensity of the incident laser beam, fluorescent particle characteristics,
camera, and the background noise of the imaging system. In practice, this depth is
usually more than the estimated penetration depth.

In a μPIV experiment, the whole flow field is illuminated, and the focal depth of
the microscope objective sets the out-of-plane resolution of the measurement. The
emitted light from the unfocused particle tracers acts as background noise for the
measurement, reducing the signal-to-noise ratio of the measurement. However, with
nPIV, the focal depth of the objective lens is larger than the penetration depth of
the evanescence wave; therefore, all the particles in the image are in focus, and
there is no background light. The brightness (size) of the particle images is a function
of their distance from the wall, where particles near the wall look bigger and brighter
than those further away. The effect of this nonuniformity in the tracer brightness
combined with the effect of Brownian motion and the near-wall velocity gradient is
discussed in detail in a recent publication
[28]. More details on TIRF, nPIV characterization, and its implementation can be found
in the literature
[22,24,25,29].

Methods

Objective-based TIRF

Fluorescence microscopy differs from most traditional techniques in that the light
of the microscope output, emitted light from the object under study, differs from
the excitation light of the light source. TIRF microscopy is generally conducted in
a laboratory using prism or objective-based methods. In this work, the near-wall nPIV
flow measurements were carried out in a microchannel using an objective-based TIRF.
Figure
2 shows the schematic of the optical arrangement used in this work. In the objective-based
TIRF, the excitation laser beam first passes through a lens arrangement to fall on
the dichroic filter cube placed inside the epi-fluorescence microscope. The filter
cube reflects the beam at the back focal plane of the microscope objective at a point
away from its axis. This puts the excitation light beam at a nonzero incident angle
(θ) with respect to the optical axis of the objective. The emitted light from fluorescent
tracer particles is then collected by the microscope objective and recorded by a camera.
The dichromatic mirror removes the emission light from that of the excitation which
helps in obtaining a clear image of only the tracer particles. The nanoparticles used
in this work showed no fluorescent property, and the dichromatic mirror in the filter
cube reflects only the excitation beam from nanoparticles and removes any possible
background illumination.

Figure 2.Sketch of the optical arrangement used in attaining objective-based TIRF.

Preparation of nanofluids

One prerequisite for conducting an experimental analysis of nanofluids is to have
stable and fully dispersed nanofluids. In this work, nanofluids were prepared by a
top down approach in which commercially bought nanoparticles were mechanically dispersed
into a base fluid (in this work, water). Ultrasonic baths and homogenizers are common
tools used in breaking the agglomerates of nanoparticles compared to magnetic and
high shear stirrers
[30]. Stabilization of the nanofluids was then carried out using an electrostatic stabilization
technique where the pH of the nanofluid suspensions was kept away from the isoelectric
pH value. The pH values of the nanofluids were kept in the range of 5.5 to 6 by adding
reagent grade nitric acid. In this work, initially, appropriate amounts of SiO2 nanoparticles (approximately 20-nm average diameter, Sigma Aldrich, #637238, St.
Louis, MO, USA) were dispersed in deionized water using an ultrasonic bath (VWR ultrasonic
cleaner, VWR International, LLC, Radnor, PA, USA; 35 kHz) for 30 min. Furthermore,
this colloidal suspension was subjected to intensified ultrasonication by immersing
a probe type sonicator (QSonica S-4000, Misonix, Qsonica, LLC, Newtown, CT, USA; 20
kHz). Cyclic ultrasonic pulses were then given to the suspension for about 30 min
to achieve maximum possible de-agglomeration of particles. Four particle weight concentrations,
0.1, 0.2, 0.5 and 1 wt.%, were considered for this investigation as they exhibited
acceptable optical properties required in the experiment and a good colloidal stability
over time. In addition, all experiments were conducted within 1 hour from sonication
time to minimize any possible chances of re-agglomeration and sedimentation.

Experimental setup

nPIV experiments are usually carried out in a quartz-liquid interface for the preferred
optical property of quartz. The microchannel used in this experiment (Translume Inc.,
Ann Arbor, MI, USA) had a rectangular cross-section with a width and height of 300
and 100 μm, respectively, where the bottom wall of the channel is customized to have
a thickness of 0.12 mm. The sidewalls of the channel deviate slightly (less than 4°)
from vertical, giving the microfluidic channel a ‘nearly’ perfect rectilinear cross-section.
During the experiment, different flow rates ranging from 0.02 to 0.06 ml/min (±0.1%)
were maintained in the microchannel using a syringe pump (KDS200, KD Scientific, Holliston
MA, USA) along with a 2.5-ml gas-tight glass syringe (Hamilton, Reno, NV, USA). The
constant flow rate provided by the syringe pump passed through the microchannel via
non-expanding polymer tubing and was drained into a reservoir at atmospheric pressure.
Figure
3 shows the photographs of the experimental setup and the zoomed view of the microchannel
placed over the microscope objective.

Figure 3.Photographs of the experimental setup and microchannel. (a) Photograph of the experimental setup; (b) view of microchannel with inlet and exit ports; (c) top view of the microchannel used in this study indicating the region of interest
with a typical nPIV image obtained.

An argon-ion CW laser beam with a wavelength of 488 nm (Spectra Physics BeamLok 2060,
Spectra Physics Inc., Santa Clara, CA, USA) was used to provide excitation light in
the near-wall region. Images were obtained using an EMCCD camera (ProEM 512, Princeton
Instruments, Trenton, NJ, USA) attached to an inverted epi-fluorescence microscope
(Leica DMI6000B, Leica Microsystems Ltd., Milton Keynes, UK) via a 63× 1.47NA oil
immersion objective. The pixel resolution for the images obtained from this imaging
set up was 4 × 106 (pixel/m). The nPIV seeding particles used in the flow were 100-nm-diameter (±5%)
polystyrene fluorescent particles (F8803, Invitrogen, Carlsbad, CA, USA) having peak
excitation and emission wavelengths of 505 and 515 nm, respectively. In all the experimental
runs, the fluorescent particle concentration was maintained at a constant volume concentration
of 0.017 vol.%. Fluorescent particles were added to the nanofluid suspension and sonicated
when nanofluid samples were prepared. Thus, the nanofluid samples contain both SiO2 nanoparticles and the fluorescent particles. It should be noted that the fluorescent
particles are about five times larger than nanoparticles with a concentration one
order of magnitude lower than the nanoparticle concentration. This will minimize any
additional particle-particle interaction between the larger seeding fluorescent and
SiO2 particles.

Evanescent wave illumination was generated on the bottom quartz-water interface in
the microchannel. The angle of incidence of light in the water-quartz interface was
evaluated to be 75o, based on the numerical aperture value of the objective lens and refractive indices
at the interface. This yielded a penetration depth of zp ≅ 105 nm (Equation 2). The depth of visible region (zv) is then estimated to be approximately 310 ± 50 nm for the base fluid that corresponds
to a non-dimensional value of zv/h = 3.5 × 10−3, where h is the microchannel height. This estimation is based on the penetration depth and
the intensity value of the background noise in captured images. The depth of the visible
region, zv, gives an estimate of the position where the velocity values are measured
[25]. A typical nPIV image obtained during experimentation is shown in Figure 3c. In almost
all the cases, the signal-to-noise ratio in the obtained images were more than eight
and four for the base fluid and nanofluids, respectively.

For each experiment, 1,500 nPIV image pairs of 256 × 80 pixels were acquired with
an inter-frame time delay of 0.6 ms. The images were then post-processed using a standard
FFT-based cross correlation program that uses a 3D Gaussian peak finding algorithm
based on a Gaussian surface fit to determine the tracer particles’ displacements
[25]. The interrogation window size was set at 186 × 68 pixels with a search radius of
50 pixels. In each case, there were sufficient numbers of matched tracer particles
in the interrogation windows. In almost all cases, the displacement was observed to
be less than 5 pixels.

Results and discussion

Experiments reported in this work were conducted in two parts: (1) nanofluids bulk
flow behavior study and (2) measurement of the near-wall flow characteristics of nanofluids
in a microchannel. Initially, the rheological characteristics were studied by the
measurements of the nanofluid bulk viscosity. These measurements were used to investigate
Newtonian characteristics of the fluid to analyze the measured near-wall velocity.
It is believed that any non-homogeneous flow characteristics that may occur in nanofluids
could be cross-verified by these two experiments.

Viscosity of nanofluids

The rheological characteristics of the nanofluids were measured using a Brookfield
DV-111 Ultra Rheometer (Middleboro, MA, USA). The rheometer works on the basis of
measuring shear stress on a rotating cone-shaped spindle immersed in the test fluid.
Figure
4 shows the measured viscosity of the nanofluids (ηnf) normalized by that of the base fluid (ηbf) at different shear rates. The experiments were conducted at a fluid temperature
of 20°C ± 0.2°C, and the error bars indicate the 95% uncertainty band of the measurement.
The results of this figure are in agreement with the previous reported observations
for viscosity enhancement of nanofluids for different particle loadings
[31]. A closer observation of the results also shows that the nanofluids exhibited Newtonian
characteristics for the range of shear rates investigated. This suggests that during
near-wall fluid velocity measurement inside the microchannel, nanofluid does not show
any shear thickening or thinning effects. The Newtonian behavior of SiO2-water nanofluids also falls in line with the recent benchmarking exercise INPBE for
nanofluids
[14]. Another expected feature of a Newtonian fluid is its homogeneous nature. Any systematic
non-homogeneity of nanoparticle in the near-wall region that is associated with nanofluid
concentration in the base fluid could affect the fluid velocity profile in this region,
which is analyzed next.

Near-wall velocity measurements for nanofluids

nPIV experiments were conducted in the microchannel for the base fluid, water, and
nanofluids of different concentrations at different flow rates from 0.02 to 0.06 ml/min.
Near-wall images were captured and post-processed to evaluate the averaged velocity
values in the measurement region next to the wall. The measurement region was located
15 mm from the inlet port of the channel to ensure a fully developed flow condition
and in the middle of the microchannel width to avoid the effects of sidewalls. All
the experiments were conducted at isothermal condition with a uniform temperature
of 22°C and no bubbles present in the inlet/outlet ports and flow path. After each
experiment, the entire loop was cleaned thoroughly by rinsing and flushing with deionized
water before the next testing fluids were introduced into the microchannel.

Since the results of the experiments for nanofluids are to be compared with that of
the base fluid, efforts were taken to maintain the same experimental conditions throughout
the tests. For instance, the flow loop (the syringe pump along with all the piping
system), the microchannel (and its physical position on the microscope), the optical
setup, and the camera settings remained constant during all the experiments. Furthermore,
the optical arrangements were undisturbed, and the camera was finely focused on the
bottom channel wall with the aid of the few fluorescent particles located on the wall.

Figure
5 shows a consolidated representation of all the experimental results carried out for
nanofluids, as well as the base fluid, compared to the values predicted by the analytical
solution for a laminar flow. The analytical prediction is for a homogeneous fluid
with Newtonian characteristics averaged in the measurement region
[32]. The error bars for the selected data points represent an 85% uncertainty level that
includes the measurement uncertainty sources as explained in discussion and measurement
errors as suggested by Benedict and Gould
[33]. As explained earlier, the out-of-plane resolution of the measurement was set by
the visible region depth, zv approximately 310 ± 50 nm. The velocity values represented in Figure
5 then depict the average velocity values at a maximum distance of 310 nm from the
wall after correcting for exponential illumination intensity inherent in nPIV
[28]. It is observed that the measured near-wall velocity shows a slight enhancement when
compared with that of the base fluid. However, the level of enhancement for each dataset
is not monotonous and does not show any clear correlation to that of nanoparticle
concentration in the nanofluids. Furthermore, the velocity variations measured for
all the flow rates all fall within the experimental uncertainty values of the measurement.
Assuming a no-slip condition on the wall, the values of wall shear rate for the velocity
data shown in Figure
5 vary from 500 to 1,500 s−1.

Moreover, Figure
5 shows that even after increasing the particle loading by one order of magnitude,
the near-wall velocity variation is similar to that of the base fluid. This indicates
that nanofluids hydro-dynamically behave as a homogeneous mixture with Newtonian fluid
characteristics in the near-wall region for the length scale studied here, O(300 nm).
For the current constant flow rate setup, the increase in the viscosity of the fluid
results only in an increase in pressure drop across the channel and does not affect
the nanofluid velocity profile. However, in the case of aggregation of particles in
nanofluids, the measured near-wall velocities would be different when compared with
that of the theoretical and experimental base fluid as a result of non-homogeneous
nature of the flow. Micro-PIV results of Walsh et al.
[20] point to the same conclusion for nanofluid flow inside a microchannel. However, the
present nPIV results provide insight in the region very close to the wall. Even though
nPIV technique enables us to obtain velocities within O(100 nm) of the wall, more
analysis and attention needs to be given to various factors affecting the measurement
methodology, which is briefly described next.

Experimental uncertainties

Before concluding remarks, it is necessary to discuss possible limitations of the
nPIV method for the measurement of the near-wall velocities for nanofluids. One major
source of error that may occur is due to the change in refractive indices of the nanofluids
at various concentrations. The measured velocity represents some average velocity
of the tracer particles in the observation region, zv, as defined by the out-of-plane resolution of the measurement, zp. Since the penetration depth of the evanescent wave is a function of the refractive
index of the fluid (Equation 2), any misjudgments in the optical properties of the
nanofluids can introduce a bias in the analysis. A recent experimental study by Kim
and Kihm
[34] investigating the effective refractive index of nanofluids using a total internal
reflectometer revealed a negligible increase in the refractive index values with an
increase in nanoparticle concentration. They show that for Al2O3-water nanofluids, the refractive index increased from 1.332 to 1.335 as the particle
concentration increased from 0 to 1 vol.%. Their experimental observation matched
well with the refractive index predictions obtained from the Rayleigh scattering theory
for colloids. A similar theoretical observation can be seen for various nanofluids
in an optical property characterization study of Taylor et al.
[35]. Therefore, it can be concluded that for the present work, which has a maximum particle
volume concentration of 0.25 vol.%, the bias that may occur due to the variation in
the refractive index of the sample is negligible.

With the addition of nanoparticles to the base fluid, the optical transparency of
the nanofluids suspension is decreased. Consequently, the practical depth of visibility,
zv, would be reduced with the increase in the nanofluid concentration. For the shear
flow near the wall, when zv is reduced, only particles closer to the wall are visible and participate in the
velocity measurement. Since the fluid velocity is slower in the region closer to the
wall, the measured averaged velocity is expected to be smaller than the average velocity
obtained for the case of the larger, zv. The observed reduction of the measured velocities for the highest particle concentration
of 1 wt.% in Figure
5 may be an indication of this phenomenon. To avoid this complication, only particle
concentrations of 1 wt.% and less were considered in this work, and the obtained data
all fall into the uncertainty range of the measurement. In the future, experimental
investigations will be required to evaluate the effect of particle type and concentration
on the visible depth and the subsequent nPIV velocity measurement.

Another factor that can affect the quality of PIV images (signal-to-noise ratio) is
the effect of SiO2 nanoparticle depositing on the bottom wall of the channel where the measurement is
made. Sedimentation on the bottom channel wall can introduce more noise thereby reducing
the image quality and signal-to-noise ratio. As the nanofluids used were thoroughly
sonicated just before the experiments, this effect was highly reduced. In addition,
care is taken such that velocity experiments were conducted in a shorter period of
time, and the flow was not stopped in between for longer durations, which could enhance
particle deposition at the bottom walls.

Distinct from the above stated biases, the nPIV experimental observations at the near-wall
region suggest that nanofluids behave as a homogeneous mixture and have Newtonian
characteristics. This indirectly suggests that any convection heat transfer enhancement
associated with nanofluids may be caused due to the augmentation of nanofluid properties
following effective medium theory. However, the above statement should be taken with
some skepticism as the present experiments were done at constant temperatures, and
no heat transfer effects occurred near the wall. Experimental efforts are presently
underway in our laboratory to improve measurement uncertainties and further investigate
the effect of heat transfer in this region.

Conclusions

The present study outlines for the first time implementation of the state-of-the-art
nPIV technique for investigating the near-wall flow characteristics of nanofluids.
SiO2-water nanofluids were used in the study with particle weight concentrations varying
from 0.1 to 1 wt.%. Near-wall velocities of nanofluids were then measured for a range
of flow rates, and the results were then compared with that of analytical and experimental
values for the base fluid (water). It is observed that even though nanofluid viscosities
increased with particle loading, the near-wall velocity values were similar to that
of the base fluid in the range of the experimental uncertainties. This observation
could be attributed to the homogenous nature and Newtonian characteristics of the
suspension. Even though only cold flow studies were made in the present work, it is
believed that utilizing this near-wall measurement technique might yield more insight
into the flow physics of nanofluids, facilitating improvements in a proposed theoretical
model based on experimental observations.

Abbreviations

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

AK conducted the experiments and drafted the manuscript. RS supervised the whole work
starting from design to analysis of data and edited the manuscript. Both authors read
and approved the final manuscript.

Authors’ information

AK is a post-doctoral research associate at the Mechanical Engineering Program, Texas
A&M University at Qatar, Doha, Qatar. RS is an assistant professor at the Mechanical
Engineering Program, Texas A&M University at Qatar, Doha, Qatar

Acknowledgments

This publication was made possible by NPRP grant number 08-574-2-239 from the Qatar
National Research Fund (a member of Qatar Foundation). The statements made herein
are solely the responsibility of the authors.